Error in book or my error?

Hi, I just registered. I am a bit stucked at an example exercise. When I work out the integral (bottom of the picture) I get -V/jnπ. The two zero-limits of the integrals give both -V/jnπ , the other limits should give -2sin(nπ)/jnπ which always is zero.

Because the resolution of the above picture is a bit low I link to an extra picture.

I always assume at first that I make a mistake when I get a different result but I can't find any mistake.

@Moderators: I guess it would be better if the title would be: electronic circuits - error in book or my error?

You could massage things to replace the complex exponentials with a trig formula, or you could just take note of the fact that 'n' has to be an integer and consider what the results are when n is even and when n is odd.